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Urgent Help with Calculus!

is f(x) = 1/3-x an odd or even function?
Reply 1
Avatar for davros
davros
16
Original post by bernard96
is f(x) = 1/3-x an odd or even function?


Well, what happens when you replace x with -x? Can you relate f(-x) to f(x) in any way? Does f(x) = f(-x)? Does f(-x) = -f(x)?
Reply 2
Avatar for bernard96
bernard96
OP
when i replace x with -x,

f(-x)
= 1 / 3- (-x)
= 1 / 3 + x
= 1 / - (-3 - X)
= - ( 1/ -3-X )


Its neither right?

since f(-x) is not equal to f(x) and -f(x)?
Original post by bernard96
when i replace x with -x,

f(-x)
= 1 / 3- (-x)
= 1 / 3 + x
= 1 / - (-3 - X)
= - ( 1/ -3-X )


Its neither right?

since f(-x) is not equal to f(x) and -f(x)?

Your final answer ("neither") is correct, but your working is decidedly ambiguous. It works if your original function was f(x)=13−xf(x) = \frac{1}{3-x} and not f(x)=13−xf(x) = \frac{1}{3} - x, as I originally took it to be.

The answer to the question "is f an odd or even function?" is "no".
Reply 4
Avatar for bernard96
bernard96
OP
The original function is . Then, it is neither, correct? Thank you so much !
Original post by bernard96
...


f(x)=13−x,  f(−x)=13+x,  −f(x)=1x−3f(x) = \dfrac{1}{3-x}, \ \ f(-x) = \dfrac{1}{3+x}, \ \ -f(x) = \dfrac{1}{x-3}
Exactly.

f(x)≠f(−x)f(x) \neq f(-x) so ff isn't an even function.

f(−x)≠−f(x)f(-x) \neq -f(x) so ff isn't odd either.

Now we can conclude that ff is neither odd, nor even.
(edited 9 years ago)

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